Two equilateral triangles are drawn on the sides AB and AC of triangle ABC.[br][br]Draw the segment DC and BE. [br]Which one is longer? [br]How do they intersect?

The construction is shown below in this silent video. We can use the 'regular polygon' tool to construct an equilateral triangle on a segment. [br][br]If you are interested in this property, search for "Napoleon's Triangles".